Circular knives of this type are very thin, comparable to razor blades having a thickness of about 0.1 mm to about 0.4 mm. Such knives are all secured to a positively driven common drive shaft at predetermined spacings from knife to knife for cutting flat sheet material into narrow strips having widths in the millimeter range. More specifically, on such an apparatus sheets of leather are cut into fine leather strips. These knives must have a certain sharpness during a cutting operation for assuring a smooth cut of all strips. However, the knives can get dull quickly and it used to be quite cumbersome to sharpen these knives heretofore, because it is not unusual to have a substantial number of knives on one drive shaft, for example fifty knives on the same drive shaft. Thus, it would be desirable to be able to sharpen these knives even during a cutting operation, without the need of removing the knives or the set of knives out of the cutting apparatus.